When you neglect in a first step the s orbitals, the sigma bonding p orbital would be below the pi bonding p orbitals. However, in the second step the sigma bonding p orbital mixes with the sigma bonding s orbitals which shifts them up in energy. Also the antibonding p orbital can be shifted up by that mechanism, although the effect is weaker due to their larger energetic separation and it would not change the ordering of the orbitals.